TEACHER KNOWLEDGE CHECK · LINEAR EQUATIONS
Understand it.Explain it. Four illustrative questions connect mathematics with teaching decisions. This is a reflection tool, not a validated assessment or a certification judgment. Answers and confidence are not sent to a server or saved.
1. Which explanation best justifies subtracting 5 from both sides of 3x + 5 = 20? A term changes sign when it crosses the equals sign. Applying the same subtraction to equal quantities preserves equality. Subtraction must always precede division.2. An illustrative solution changes 3x + 5 = 20 into 3x = 25. What is the most useful first response? Ask the learner to memorize a sign-change rule. Tell the learner to divide 25 by 3. Ask what operation was applied to each side, and represent subtracting 5 from both sides.3. Why does dividing both sides of 3x = 15 by 3 isolate x? 3x means three times x, and division by nonzero 3 reverses that multiplication. Division removes every coefficient, including zero. The equals sign means the answer follows.4. Which question best checks understanding beyond obtaining x = 5? How fast did you solve it? Can you explain why each transformation preserves equality and verify the solution in the original equation? Did you remember to move the 5?How confident are you explaining why equation-solving steps work? Not yet confident Somewhat confident ConfidentReview my responses →